What is the square of a column vector?

[devonho]

Homework Statement

Hi,

Is there a matrix property that can be applied to take the square of a column vector?

Something like:

{\bf x}=\left[x_1,x_2,x_3\right]^T
\left[{\bf x}\right]^2
={\bf x}{\bf x}^T
or
={\bf x}^T{\bf x}?

Thank you.

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

Hi,

Is there a matrix property that can be applied to take the square of a column vector?

Something like:

{\bf x}=\left[x_1,x_2,x_3\right]^T
\left[{\bf x}\right]^2
={\bf x}{\bf x}^T
or
={\bf x}^T{\bf x}?

Thank you.
...

What is the size of the matrix: ={\bf x}{\bf x}^T\,?

What is the size of the matrix: ={\bf x}^T{\bf x}\,?

 

[devonho]

Hi SammyS,

{\bf x}{\bf x}^T is 3x3
while
{\bf x}^T{\bf x} is 1x1

 

[murmillo]

I'm not sure what you mean by the square of a column vector...

 

[SammyS]

Generally the square of a vector refers to the scalar product, which you can crudely think of as a 1 by 1 matrix. Therefore, the answer is (x^T)x .